Estimation of circadian rhythm components using auto?regressive modelling methods

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Abstract
The use of auto‐regressive modelling for the analysis of circadian and related rhythms is presented as an alternative to the Gosinor, periodogram and auto‐correlation methods. The method is particularly well suited to short time‐series corrupted with non‐white noise and containing multiple rhythm frequencies. Estimation of the model coefficients is via a direct least‐squares algorithm and the frequencies are determined by standard factorisation of the resulting polynomial. Results on simulated data and rat locomotor activity show the feasibility of the method, and indicate how the parameters of model order and sampling rate can be selected to obtain optimum frequency resolution and bandwidth. The method can be implemented using recursive algorithms which avoid matrix inversion and give faster computation, and extension to Maximum Entropy methods is under current investigation.